Below is a simple version of the timelines using only film canon which is color coded to show when timelines change and stay the same between each other.
T1C: Resistance fighter escapes from prison camp and joins with John Connor's Resistance. While the fighter is assaulting Skynet's core, the resistance HQ is attacked killing both Kyle Reese and John Connor. The lone resistance fighter uploads a virus into Skynet, who has been using the Temporal Data Transmitting System (TDTS) to send code back in time to an earlier version of itself thus speeding up its capability and abilities. The virus created by resistance fighter Dr. Hanover, infects Skynet and thus infecting the earlier version of itself causing Judgement Day to cease to exist and creating a peaceful 2015 (T: Future Shock VG)